An air puck of mass 0.33 kg is tied to a
string and allowed to revolve in a circle of radius 1.12 m on a horizontal, frictionless table.
The other end of the string passes through a
hole in the center of the table and a mass of
1.1 kg is tied to it. The suspended mass remains in equilibrium while the puck revolves.
The acceleration of gravity is 9.8 m/s
2.What is the horizontal force acting on the
puck?
To find the horizontal force acting on the puck, we need to analyze the forces acting on the system.
1. Centripetal Force: The puck is moving in a circular path, so there must be a centripetal force acting on it to keep it moving in that path. The centripetal force is given by the equation: Fc = (m*V^2) / R, where m is the mass of the puck, V is its velocity, and R is the radius of the circular path. Since the velocity is not provided, we need to find it.
2. Velocity of the puck: We can find the velocity of the puck using the equation: V = (2πR) / T, where T is the period of revolution. The period is the time it takes for the puck to complete one full revolution, which can be found using the equation: T = 2π / ω, where ω is the angular velocity. The angular velocity can be found using the equation: ω = √(g / R), where g is the acceleration due to gravity.
3. Forces in equilibrium: The system is in equilibrium, which means the forces acting on the system must be balanced. The tension in the string caused by the hanging mass is equal to the centripetal force required to keep the puck moving in a circular path.
Now, let's calculate the values step by step:
1. Angular velocity (ω):
ω = √(g / R)
= √(9.8 / 1.12)
≈ 3.004 rad/s
2. Period of revolution (T):
T = 2π / ω
= 2π / 3.004
≈ 2.093 s
3. Velocity of the puck (V):
V = (2πR) / T
= (2π * 1.12) / 2.093
≈ 3.370 m/s
4. Centripetal force (Fc):
Fc = (m * V^2) / R
= (0.33 * 3.370^2) / 1.12
≈ 3.348 N
Since the suspended mass remains in equilibrium with the puck, the tension in the string is equal to the centripetal force calculated above. Therefore, the horizontal force acting on the puck is approximately 3.348 N.